Research and Application of Trigonometric Leveling to Replace Precise Leveling
Publication: Journal of Surveying Engineering
Volume 147, Issue 3
Abstract
Aiming at the low efficiency of precise geodetic leveling in tough terrain, we propose a precise trigonometric leveling (PTL) method to replace first-order Class II leveling. First, we analyze the errors of unidirectional trigonometric leveling and list corresponding ways to reduce those errors. Then, the practical formula of PTL is introduced that combines the simultaneous reciprocal observation with the leap-frog method to reduce the effect of atmospheric refraction. Besides, the PTL method uses two robotic total stations to perform an even number of reciprocal observations to avoid measuring the heights of instruments. Finally, two experiments are conducted using the PTL method; one is river-crossing precise leveling, and the other is highland precise leveling. Compared with the precise geometric leveling in the 25 km of the leveling circuit, the result shows that the standard deviation per kilometer of PTL is , which is less than and proves that PTL can achieve first-order Class II leveling precision to some degree conditions.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All raw data that support the findings of this study are available from the corresponding author upon reasonable request, and the trial software of data collection can be available from the corresponding author.
References
Ceylan, A., and O. Baykal. 2006. “Precise height determination using leap-frog trigonometric leveling.” J. Surv. Eng. 132 (3): 118–123. https://doi.org/10.1061/(ASCE)0733-9453(2006)132:3(118).
Ceylan, A., and O. Baykal. 2008. “Precise height determination using simultaneous-reciprocal trigonometric levelling.” Surv. Rev. 40 (308): 195–205. https://doi.org/10.1179/003962608X290997.
Chrzanowski, A. 1983. Economization of vertical control surveys in hilly areas by using modified trigonometric levelling. Washington, DC: American Congress on Surveying and Mapping.
Dodson, A. H., and M. Zaher. 2013. “Refraction effects on vertical angle measurements.” Surv. Rev. 28 (217): 169–183. https://doi.org/10.1179/sre.1985.28.217.169.
Holdahl, S. R. 1981. “A model of temperature stratification for correction of leveling refraction.” Bull. Géodésique 55 (3): 231–249. https://doi.org/10.1007/bf02530864.
Kahmen, H., and W. Faig. 1988. Surveying. Berlin: Walter de Gruyter.
Kirschner, H., and W. Stempfhuber. 2008. “The kinematic potential of modern tracking total stations-a state of the art report on the Leica TPS1200+.” In Proc., 1st Int. Conf. on Machine Control & Guidance, 51–60. Zürich, Switzerland: ETH Zurich.
Leveling, G. 1981. NOAA manual NOS NGS 3. Washington, DC: National Oceanic and Atmospheric Administration.
Li, Y. 1990. Corrections for atmospheric refraction in precise leveling. New York: Springer.
Merkle, W. J., and J. J. Myers. 2004. “Use of the total station for load testing of retrofitted bridges with limited access.” In Vol. 5391 of Proc., Smart Structures and Materials 2004: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, 687–694. Bellingham, Washington: International Society for Optics and Photonics.
Mozzhukhin, O. A. 2001. “Refraction in leveling and a method for its determination—Theoretical basis.” Acta Geod. Geophys. Hung. 36 (3): 297–312. https://doi.org/10.1556/AGeod.36.2001.3.6.
Pellegrinelli, A., A. Furini, M. Bonfe, and P. Russo. 2013. “Motorised digital levels: Development and applications.” Surv. Rev. 45 (330): 174–189. https://doi.org/10.1179/1752270612Y.0000000039.
Rüeger, J. M. 1995. “EDM-height traversing: Refraction correction and experiences.” Aust. Surveyor 40 (4): 48–56. https://doi.org/10.1080/00050334.1995.10558562.
Rüeger, J. M., and F. K. Brunner. 1981. “Practical results of EDM-height traversing.” Aust. Surveyor 30 (6): 363–373. https://doi.org/10.1080/00050326.1981.10441212.
Schomaker, M. C. 1981. Geodetic leveling. Washington, DC: US Dept. of Commerce, National Oceanic and Atmospheric Administration.
Shen, Y., T. Huang, X. Guo, Q. Zang, and M. Herrero-Huerta. 2017. “Inversion method of atmospheric refraction coefficient based on trigonometric leveling network.” J. Surv. Eng. 143 (1): 06016002. https://doi.org/10.1061/(ASCE)SU.1943-5428.0000199.
Zhenglu, Z., Z. Kun, D. Yong, and L. Changlin. 2005. “Research on precise trigonometric leveling in place of first order leveling.” Geo-spatial Inf. Sci. 8 (4): 235–239. https://doi.org/10.1007/BF02838654.
Zhou, J., H. Xiao, W. Jiang, W. Bai, and G. Liu. 2020. “Automatic subway tunnel displacement monitoring using robotic total station.” Measurement 151 (Feb): 107251. https://doi.org/10.1016/j.measurement.2019.107251.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 147 • Issue 3 • August 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jun 19, 2020
Accepted: Apr 16, 2021
Published online: Jun 8, 2021
Published in print: Aug 1, 2021
Discussion open until: Nov 8, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Jun Xiao, Jianping Xian, Song Li, Shuai Zou, Research on Elevation Survey Method of Sea-Crossing Bridge under Adverse Conditions, Sustainability, 10.3390/su141811641, 14, 18, (11641), (2022).
- Jianguo Zhou, Chao Luo, Weiwei Jiang, Xianyu Yu, Peng Wang, Using UAVs and robotic total stations in determining height differences when crossing obstacles, Measurement, 10.1016/j.measurement.2021.110372, 188, (110372), (2022).